Complete the following tasks for this equation:

Question

b/7.8=-2.15



Give an estimate for the solution. Be sure to explain how you arrived at the estimate, either by showing an equation or in words.
Solve the equation. Show or explain your work.
Compared to your estimate, is your answer reasonable? Explain your answer in complete sentences.

Answer 1

Step 1: Estimate the Solution

The equation given is

\[ \frac{b}{7.8} = -2.15 \]

To estimate the value of \(b\), we can multiply both sides by 8 (a close estimation of 7.8) to simplify our calculations. Thus, we have:

\[ b \approx -2.15 \times 8 \]

Calculating this gives:

\[ -2.15 \times 8 = -17.2 \]

So, our estimate for \(b\) is approximately \(-17.2\).

Step 2: Solve the Equation

Now, let’s solve the equation exactly. We start from the original equation:

\[ \frac{b}{7.8} = -2.15 \]

To isolate \(b\), we can multiply both sides by 7.8:

\[ b = -2.15 \times 7.8 \]

Now let’s perform the multiplication:

\[ b = -16.83 \]

Step 3: Comparison of Estimate and Actual Answer

Our estimate for \(b\) was \(-17.2\) and we found the exact solution to be \(-16.83\).

Comparing the two:

• Estimate: \(-17.2\)
• Exact Solution: \(-16.83\)

The exact solution of \(-16.83\) is quite close to the estimate of \(-17.2\), indicating that our estimation method was effective.

Conclusion

In conclusion, my estimation was reasonably close to the actual solution of the equation. The estimate of \(-17.2\) gave a good approximation, as \(-16.83\) is only slightly higher than \(-17.2\). This demonstrates that using a rounded number for calculations can provide a useful initial insight into the solution.

Answer 2

can you make it less advanced

Answer 3

Sure! Let's break it down into simpler steps.

Step 1: Estimate the Solution

The equation we have is:

\[ \frac{b}{7.8} = -2.15 \]

To estimate \(b\), we can round \(7.8\) to \(8\), which is easier to work with. So, we can think about it like this:

We want to find out what \(b\) would be if \(b\) divided by \(8\) equals \(-2.15\).

So, we can write:

\[ b \approx -2.15 \times 8 \]

Now let's do the multiplication:

\[ -2.15 \times 8 = -17.2 \]

Thus, our estimate for \(b\) is about \(-17.2\).

Step 2: Solve the Equation

Now, let’s solve the equation exactly. We start from:

\[ \frac{b}{7.8} = -2.15 \]

To solve for \(b\), we can multiply both sides by \(7.8\). This helps us get \(b\) by itself. It looks like this:

\[ b = -2.15 \times 7.8 \]

Now we calculate that:

\[ -2.15 \times 7.8 \approx -16.83 \]

So the exact solution is \(b = -16.83\).

Step 3: Compare Estimate and Exact Answer

We estimated that \(b\) is about \(-17.2\) and found out that the exact answer is \(-16.83\).

• Estimate: \(-17.2\)
• Exact Answer: \(-16.83\)

The exact answer, \(-16.83\), is very close to our estimate of \(-17.2\). This means our estimation method worked pretty well!

Conclusion

In summary, our estimate of \(-17.2\) was a good guess because it is close to the actual solution of \(-16.83\). This shows that sometimes rounding numbers can help make calculations easier and still provide a reasonable answer!

Answer 4

can you use lees words and mae it just a little less advanced

Answer 5

Of course! Here’s a simpler version with fewer words:

Step 1: Estimate the Solution

We have the equation:

\[ \frac{b}{7.8} = -2.15 \]

To estimate \(b\), round \(7.8\) to \(8\). So, we multiply:

\[ b \approx -2.15 \times 8 = -17.2 \]

Step 2: Solve the Equation

Now, let’s find the exact answer. From the original equation:

\[ \frac{b}{7.8} = -2.15 \]

Multiply both sides by \(7.8\):

\[ b = -2.15 \times 7.8 \]

Calculating gives:

\[ b = -16.83 \]

Step 3: Compare Estimate and Exact Answer

• Estimate: \(-17.2\)
• Exact Answer: \(-16.83\)

The exact answer \(-16.83\) is close to the estimate \(-17.2\).

Conclusion

Our estimate was pretty good! It shows that rounding can help us get a useful answer.